Topological Echoes of Primordial Physics in the Universe at Large Scales

Alex Cole, Matteo Biagetti, Gary Shiu

Keywords: persistent homology, persistence images, statistical inference, cosmology, non-gaussianity

TL;DR: We use persistent homology to compute how cosmological initial conditions are imprinted on the late-time distribution of galaxies, validating our pipeline by "detecting" primordial non-Gaussianity in a set of dark matter simulations.

Abstract: We present a pipeline for characterizing and constraining initial conditions in cosmology via persistent homology. The cosmological observable of interest is the cosmic web of large scale structure, and the initial conditions in question are non-Gaussianities (NG) of primordial density perturbations. We compute persistence diagrams and derived statistics for simulations of dark matter halos with Gaussian and non-Gaussian initial conditions. For computational reasons and to make contact with experimental observations, our pipeline computes persistence in sub-boxes of full simulations and simulations are subsampled to uniform halo number. We use simulations with large NG ($f_{\rm NL}^{\rm loc}=250$) as templates for identifying data with mild NG ($f_{\rm NL}^{\rm loc}=10$), and running the pipeline on several cubic volumes of size $40~(\textrm{Gpc/h})^{3}$, we detect $f_{\rm NL}^{\rm loc}=10$ at $97.5\%$ confidence on $\sim 85\%$ of the volumes for our best single statistic. Throughout we benefit from the interpretability of topological features as input for statistical inference, which allows us to make contact with previous first-principles calculations and make new predictions.

Previous Submission: No

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/topological-echoes-of-primordial-physics-in/code)